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# Communications in Information and Systems

## Volume 21 (2021)

### Number 2

### Applications of the Girsanov theorem for multivariate fractional Brownian motions

Pages: 269 – 296

DOI: https://dx.doi.org/10.4310/CIS.2021.v21.n2.a5

#### Authors

#### Abstract

In this article, multivariate fractional Brownian motions with possibly different Hurst indices in different coordinates are considered and a Girsanov-type theorem for these processes is given. Two applications of this theorem to stochastic differential equations driven by multivariate fractional Brownian motions are presented. The first is an existence result for weak solutions to stochastic differential equations with a drift coefficient that can be written as a sum of a regular and singular part and an autonomous diffusion coefficient. The second application concerns a maximum likelihood estimate of a drift parameter in stochastic differential equations with additive multivariate fractional noise.

#### Keywords

multivariate fractional Brownian motion, stochastic differential equation, Girsanov theorem, weak solution, drift parameter estimation

#### 2010 Mathematics Subject Classification

60G22, 60H10

Received 10 June 2020

Published 3 June 2021